Full Three-Dimensional Motion Characterization of a Gimballed Electrostatic Microactuator Christian Rembe, Lilac Muller, Richard S. Muller, Roger T. Howe Berkeley Sensor&Actuator Center, University of California at Berkeley 497 Cory Hall; Berkeley, CA 94720 510-642-6256; fax: 510-643-6637; e-mail:
[email protected]
PURPOSE
of this three-dimensional motion-characterization method by studying the response of a micromachined gimballed actuator developed for a hard-disk-drive application.
Advanced testing methods for the dynamics of microdevices are necessary to develop reliable marketable microelectromechanical systems (MEMS). The main purpose for MEMS testing is to provide feedback to the design-and-simulation process in an engineering development effort. This feedback should include device behavior, system parameters, and material properties. An essential part of a more effective microdevice development is high-speed visualization of the dynamics of MEMS structures. We have developed and employed a full three-dimensional-motion-characterization system for MEMS to observe the response of a gimballed microactuator, a multi-degree-of-freedom microdevice. [Keywords: MEMS testing, interferometry, stroboscopy, image processing, hard-disk drives]
The measurement of pure out-of-plane deflections can also be performed with a commercially available Laser-Doppler-Scanning Vibrometer from Polytec PI [7,8]. This system measures the velocity of a moving surface via the Doppler frequency shift of a reflected Laser beam. The displacement at a single spot of the surface under investigation is computed by integrating the velocity measurement. However, the vibrometer can only measure one-dimensional motion. Full three-dimensional, rigid-body motion can be investigated with a commercially available Networked Probe Station from Umech [9]. This system is a stroboscopic microscope. A periodic motion of a microstructure, which is imaged with a microscope on a CCD camera, is frozen with a strobed light. Digital image processing is used to calculate the sub-pixel-in-plane motion. With an additional interferometric technique out-of-plane motion is measured. The Umech system is capable of measuring three-dimensional, rigid-body motion, while the system presented in this paper is capable for the first time of measuring rigid-body, in-plane motion together with out-of-plane-deflection maps of a vibrating device surface in a single experiment.
INTRODUCTION MEMS are typically characterized by comparing the system output with a defined input function. For example, in the case of an electrostatic actuator with an integrated sensor, the input driving voltage is compared with the signal of the capacitive sensor that corresponds to the actuator displacement. Static characteristics as well as frequency-response behavior can be investigated with these methods, but it does not provide knowledge about any failure mechanisms of the microactuators. The dynamics of microstructures have to be studied using optical-measurement techniques for this information [1,2]. In the example of an electrostatic actuator, failure modes might result from excitation of mechanical modes that interfere with the pure deflection motion.
STROBOSCOPIC MICROSCOPIC INTERFEROMETER In reference [5] we demonstrate a stroboscopic, computercontrolled, phase-shifting interferometer in high-resolution measurements of out-of-plane motions. In this paper, we describe a system for full three-dimensional motion characterization.
In this paper we present a new microscopic stroboscopic interferometer system that allows the full three-dimensional-motion measurement of rapidly moving microstructures. The interaction of mechanical modes that move in plane with the out-of-planedeflection modes can be investigated with our system. The system extracts in-plane, rigid-body motion by employing digital-image processing with a resolution better than 5nm. In addition, the system can measure out-of-plane-deflection maps at defined time points of a periodical motion using interferometric techniques. Out-of-plane displacement can be measured with a resolution better than 1nm. Inplane and out-of-plane motions are measured together in a single experiment and with high precision. This new system is capable of measuring periodic or reproducible transient processes.
Setup The schematic of the new three-dimensional Stroboscopic Microscopic Interferometer System (SMIS) is shown in Figure 1.
Extraction of MEMS in-plane, rigid-body motion from a pseudocinematographic image sequence has been reported in [3,4]. We use a similar technique for the in-plane-motion determination. The algorithm reported previously is capable of extracting in-plane displacements between two images that correspond to less than a digital pixel. The algorithm presented in this paper extracts reliable in-plane deflections over several pixels with sub-pixel resolution. The measurement of out-of-plane deflections using a stroboscopic interferometer system has been presented by us in [5,6]. Our new system combines the out-of-plane deflection measurement with a new in-plane motion-measurement feature. We demonstrate the use 0-7803-6587-9/01/$10.00 ©2001 IEEE
FIGURE 1. SCHEMATIC OF STROBOSCOPIC INTERFEROMETER SYSTEM. THE ABBREVIATIONS USED ARE AS FOLLOWS: L – l/2- WAVE-PLATE, P – POLARIZER, PBS – POLARIZATION BEAM SPLITTER, fc – CONDENSER LENS, fi – IMAGING LENS, AND fm – MICROSCOPE OBJECTIVE FOR IMAGING, LD – LASER DIODE, M – REFERENCE MIRROR 91
IEEE 01CH37167. 39th Annual International Reliability Physics Symposium, Orlando, Florida, 2001
first region defines the region for the in-plane algorithm. The second region has to be inside the region for the algorithm (ROA) and is termed in Figure 3 as region of interest (ROI). The ROI must be a part of image 1 that shows only the moving structure. The algorithm can only work properly if the structure of the image part in ROI is not deformed somewhere in the ROA of the remaining images of set 1. This is the demand on the definition of ROA that must be ensured by the user. If the ROA is too big, the computation time increases unnecessarily.
The new system can be conveniently used as common light microscope if the light beam that goes to the reference mirror is shadowed with shutter S. Through the stroboscopic visible-light illumination, a set (set 1) of images is taken of the periodic motion without forming an interference pattern. We have developed a new algorithm to extract the in-plane motion from this sequence with a subpixel resolution better than 5nm. After the system has taken a set of images (set 1) without interference fringes the shutter is moved out of the laser beam. Now the system is an interferometer and a set of images (set 2) is taken. The interferometer forms an image of the MEMS device that is crossed by bright and dark fringes that can be interpreted as a contour map of object surface heights. The optical arrangement is that of a Twyman-Green interferometer and is described in detail in [5,6]. To measure the shape of a static specimen or that of a moving specimen, “frozen” by the strobe light, phase-shifting interferometry (PSI) is used.
In the following, the algorithm for in-plane computation is explained on the example of two images in set 1. The restrictions for the definition of ROA and ROI are specified in Figure 3. For in-plane motion, SMIS can only measure rigid-body motion. The reason for this restriction is that the algorithm can only calculate the in-planetranslational motion of an undeformed structure on the moving specimen in the ROI.
A five-step PSI algorithm (Hariharan’s Algorithm) in which the fringe pattern of a specimen is visualized five times for five different reference-mirror positions is used [6]. The translation data extracted from set 1 are then used to recalculate the in-plane motion from the images of set 2. Finally, the out-of-plane motion is calculated with nm resolution using the five-step-PSI algorithm. Set 2 contains five images for every single time point where the surface-height map is measured because of the five-step-PSI method. Therefore, to investigate the three-dimensional deflection at 10 time points the systems saves 10 images for the in-plane-motion extraction and 5 times 10 images for the out-of-plane-motion computation. Therefore, full sequence for a measurement at 10 time points contains 60 images.
Analysis Software The structure of the algorithm, which computes full threedimensional motion, is presented using analysis software written â with MATLAB (The MathWorks, Inc) and is shown in Figure 2.
FIGURE 3. DEFINITION AND RESTRICTION OF ROA AND ROI. THE IMAGE SIZE IS DEFINED THROUGH THE RECTANGULAR FRAME. We number the columns of each picture with in and the rows with jn ( in , jn ÎÀ ). In opposite to the common way row number jn=1 is at the bottom of the image. Column number in=1 is at the first column at the left side as usual. The advantage of this definition is that we can define a coordinate system i and j ( i, j ÎÂ ) that coincides for integer values with the numbers of the columns in and rows jn. The displacement di and dj in Figure 3 are computed using digital-image processing. The Progressive-Scan-CCD camera captures 8-bit gray-level images that are saved as TIF-files on the â hard disk. They are transformed to matrices using MATLAB . In digital-image processing an image is defined as the continuous gray-level-distribution function I(i,j) that one would get with an image sensor having infinite small pixels with the same characteristic as the CCD camera [10]. We use this definition for image in the following. The sampled-image matrix M with components Is(in,jn) is the â
TIF-image or MATLAB matrix and the resampled image Ir(i,j) is the continuous gray-level distribution function that can be calculated from the sampled image by employing the Nyquist-Sampling Theorem. Equation 1 demonstrates this for a sampled image with n columns and m rows.
FIGURE 2. STRUCTURE OF THE ANALYSIS SOFTWARE
Algorithm for In-plane-Motion Computation The user has to specify two regions in the first image of set 1 (image 1) before the in-plane displacement can be calculated. The
92
sin F k - i I s k , jn F k - i k =1
shifted about k pixels by employing operation (4) a shift to the right about i Î Â , i ³ 0 is expressed by
n
f i, l = å
(1)
sin F l - j I r (i, j ) = å f i, l i F l - j l =1 m
M i = i - k M k + k + 1 - i M k +1 ,
when k is the greatest integer which is smaller than i ((i-k)
